Refined Telluric Absorption Correction for Low-resolution Ground-based Spectroscopy: Resolution and Radial Velocity Effects in the O₂ <i>A</i>-band for Exoplanets and K i Emission Lines

Telluric correction of spectroscopic observations is either performed via standard stars that are observed close in time and airmass along with the science target, or recently growing importance, by theoretical telluric absorption modeling. Both approaches work fine when lines resolved, i.e. at spectral resolving power larger than about 10000, it sufficient to facilitate detection features lower resolution. However, a meaningful quantitative analysis requires also reliable recovery line strengths. Here, we show for Fraunhofer A-band molecular O2 approach fails this resolutions, as an example general problem. Doppler-shift dependent errors restored flux may arise, which can amount more 50% extreme cases, depending on shapes target features. Two applications discussed: O2-band reflected light Earth analog atmosphere, facilitated potentially future using orbiting starshade ground-based extremely large telescope; intrinsic ratio K I post-nova V4332 Sgr tracing optical depth emitting region, exemplify relevance present-day instrumentation. We how one should derive functions compensation error dependence radial velocity shift, resolution line-profile function use high atmospheric transmission modeling, has be solved individual case.